*There is a lot more to matrix analysis than this - see for example SingularValueDecomposition.*
and also

http://en.wikipedia.org/wiki/Matrix_theory

If the

EigenValue's magnitude is greater than 1,
it equals (1 + interest rate) [

*or 1 + growth rate if that's clearer to you*].

If the

EigenValue's magnitude is less than 1,
it equals (1 - decay rate).

If the

EigenValue's magnitude is 1, the system neither grows nor decays.
It might flip-flop or cycle, though.

If the

EigenValue is a complex number,
it indicates a cycling system.

*How about combinations of EigenValues? It's not all scaling; what makes multiplication by one matrix do a reflection, and another a rotation?*
If the

EigenValue is -1,
multiplying by it does a reflection
(which is also a 180 degree rotation).

If the

EigenValue is a negative real number,
multiplying by it does a reflection (and a scaling).

If the

EigenValue is i,
multiplying by it is the same as rotating 90 degrees.
After 2 rotations, you will do a reflection.
After 4 rotations,
you will wrap all the way around.
This is a cycle.

If the

EigenValue is a complex number,
multiplying by it does a rotation (and a scaling).
After several rotations,
you will eventually wrap all the way around.
This is a cycle.

An online Matrix Calculator is at

http://wims.unice.fr/wims/wims.cgi?session=3G0DBDBD76.5&+lang=en&+module=tool%2Flinear%2Fmatrix.en

See also

CategoryMath